Airlines still need to invest in the fuel efficiency of their fleets, despite the low price of oil, Airbus' chief operating officer told CNBC on Tuesday.

"The price of fuel is a double-edged sword," John Leahy told CNBC on Tuesday.

Oil prices have declined further since the start of 2016 to around the $31-mark. Low oil prices could deter airlines from investing in newer, more fuel-efficient models, such as Airbus' A320 NEO, but Leahy remained confident that airlines would make investments at a time of higher profits.

"When the price is high, airlines aren't making money but they desperately want new aircraft that they can't afford to pay for. (But) I think they understand that now when the price of fuel is low, they're making record profits and they know that they need to provision for the future and they're placing orders as well for these new fuel-efficient airplanes."

Earlier Airbus said its planemaking division recorded 1,036 net plane orders after cancellations, down 29 percent from 2014, compared with Boeing's tally of 768, a fall of 46 percent.

Despite falling behind rival Boeing in terms of deliveries, Leahy said that it won't take long for the planemaker to catch up.

"I think almost all the orders will be delivered but we don't build the airplanes on speculation."

"We build airplanes to spec so when we increase production it's because we already have legally binding contracts for those aircraft."

ERIC PIERMONT/AFP/Getty Images

Airbus Chief Operating Officer John Leahy

In particular, Airbus has experienced a delay in delivering its latest fuel-efficient model, the A320 NEO ("New Engine Option"), but Leahy said the delay amounted to a matter of weeks.

"We should be delivering the first airplane in a couple of weeks, definitely before the end of January," he said.

Leahy said the company had been "managing the order book relatively well" since 2005. "We're very proud of that, our production has not gone up and down, it has stayed relatively flat and is ramping up quite nicely."